Geometry of $[\varphi,\vec{e}_{3}]$-minimal surfaces in $\mathbb{R}^{3}$

TL;DR

This survey presents a systematic geometric approach to studying $[{ ext{ extphi}}, ext{ extbf{e}}_{3}]$-minimal surfaces in three-dimensional space, highlighting recent fundamental results in the field.

Contribution

It introduces a comprehensive framework for analyzing $[ ext{ extphi}}, ext{ extbf{e}}_{3}]$-minimal surfaces and summarizes recent key findings.

Findings

Development of a general geometric approach

Fundamental results in the theory of $[ ext{ extphi}}, ext{ extbf{e}}_{3}]$-minimal surfaces

Recent advances in understanding these surfaces

Abstract

In this survey we report a general and systematic approach to study $[\varphi,\vec{e}_{3}]$-minimal surfaces in $\mathbb{R}^{3}$ from a geometric viewpoint and show some fundamental results obtained in the recent development of this theory.